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Estimating Measurements

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Estimating Measurements

The school radio station is planning a new studio layout. Use sensible benchmarks and estimation to check whether the equipment will fit. Unless a question says otherwise, give units and show enough working to explain your reasoning.

Part A: Choose and justify

Select the best estimate in each question. Think about the size of familiar objects before calculating.

1.Georgia is checking whether a microphone cable can reach across the studio. Which is the most sensible estimate for the width of a small studio room?

0.4 m
4 m
40 m
400 m

2.A sound-mixing desk top is roughly 1.8 m long and 0.7 m deep. Which is the best estimate of its area?

0.13 m²
1.3 m²
13 m²
130 m²

3.Tui estimates a 2-litre drink bottle holds 200 cm³. Is that a reasonable estimate? Choose the best response.

Yes; 2 litres is about 200 cm³.
No; 2 litres is about 2,000 cm³.
No; 2 litres is about 20,000 cm³.
No; 2 litres is about 200,000 cm³.

4.Which two are useful benchmarks for estimating the length of equipment in the studio? Select both.

A standard 30 cm ruler
The approximate height of a door, about 2 m
The mass of a 1 kg bag of rice
The temperature of a room, about 20°C

Part B: Estimate, calculate, evaluate

Use benchmarks and appropriate rounding. An estimate should be plausible, not just a calculation with a guessed number.

5.Aisha needs a storage crate for headphones. Estimate the volume of a crate measuring about 40 cm × 30 cm × 25 cm. Give your answer in cm³ and litres.

6.A foam panel is about 1.2 m long and 0.8 m wide. Estimate its area in m². Explain one way to check whether your answer is a sensible size.

7.Georgia estimates a cable is 3.5 m long. When measured, it is 4.0 m. Calculate the percentage error using the measured length as the reference value. Show the calculation.

8.A studio wall is approximately 5 m long and 2.5 m high. Estimate its area. Then state why measuring to the nearest centimetre would not be useful when only a rough estimate is needed.

9.Two estimates are given for the volume of a padded equipment case: 0.03 m³ and 30 m³. Which is more plausible for a case that is about 60 cm × 40 cm × 20 cm? Explain and include a calculation.

10.Plan a quick estimating method for the length of a microphone stand without using a measuring tape. Name a familiar benchmark, give a possible estimate, and explain how you would check it later.

11.Aisha estimates a rectangular notice panel is 1.5 m². Its actual dimensions are 1.0 m by 1.2 m. Is her estimate an overestimate or underestimate, and by what percentage of the actual area?